Oracle and Adaptive Compound Decision Rules for False Discovery Rate Control
Wenguang Sun and Tony Cai
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Abstract:
We develop a compound decision theory framework for multiple testing
problems and derive an oracle rule based on the z-values that
minimizes the false non-discovery rate (FNR) subject to a constraint
on the false discovery rate (FDR). It is shown that many commonly
used multiple testing procedures, which are p-value based, are
inefficient. An adaptive procedure based on the z-values is
proposed. It is shown that the z-value based adaptive procedure
asymptotically attains the performance of the z-value oracle
procedure and is more efficient than the conventional p-value
based methods. Numerical performance of the adaptive procedure is
investigated using both simulated and real data. In particular our
method is demonstrated in an analysis of the microarray data from a
HIV study that involves testing a large number of hypotheses
simultaneously.
- Paper:
pdf file.
- R codes for the adaptive testing procedure.
Here is the readme file.
- Other related papers:
Cai, T., Jin, J. & Low, M. (2007).
Estimation and confidence sets for sparse normal mixtures.
The Annals of Statistics 35, 2421-2449.Jin, J. & Cai, T. (2007).
Estimating the null and the proportion of non-null effects in large-scale multiple comparisons.
J. American Statistical Association 102, 495-506.Sun, W. and Cai, T. (2009).
Large-Scale Multiple Testing under Dependency.
J. Royal Statistical Society, Series B 71, 393-424.